**Distributional Generalization** is a type of generalization that roughly states that outputs of a classifier at train and test time are close as distributions, as opposed to close in just their average error. This behavior is not captured by classical generalization, which would only consider the average error and not the distribution of errors over the input domain.

**Spatial Gating Unit**, or **SGU**, is a gating unit used in the [gMLP](https://paperswithcode.com/method/gmlp) architecture to captures spatial interactions. To enable cross-token interactions, it is necessary for the layer $s(\cdot)$ to contain a contraction operation over the spatial dimension. The layer $s(\cdot)$ is formulated as the output of linear gating:

$$
s(Z)=Z \odot f\_{W, b}(Z)
$$

where $\odot$ denotes element-wise multiplication. For training stability, the authors find it critical to initialize $W$ as near-zero values and $b$ as ones, meaning that $f\_{W, b}(Z) \approx 1$ and therefore $s(Z) \approx Z$ at the beginning of training. This initialization ensures each [gMLP](https://paperswithcode.com/method/gmlp) block behaves like a regular [FFN](https://paperswithcode.com/method/gmlp) at the early stage of training, where each token is processed independently, and only gradually injects spatial information across tokens during the course of learning.

The authors find it further effective to split $Z$ into two independent parts $\left(Z\_{1}, Z\_{2}\right)$ along the channel dimension for the gating function and for the multiplicative bypass:

$$
s(Z)=Z\_{1} \odot f\_{W, b}\left(Z\_{2}\right)
$$

They also normalize the input to $f\_{W, b}$ which empirically improved the stability of large NLP models.

Spatial Gating Unit

Pay Attention to MLPs

Distributional Generalization

Distributional Generalization: A New Kind of Generalization

**Softsign** is an activation function for neural networks:

$$ f\left(x\right) = \left(\frac{x}{|x|+1}\right)$$

Image Source: [Sefik Ilkin Serengil](https://sefiks.com/2017/11/10/softsign-as-a-neural-networks-activation-function/)

Source	Distributional Generalization: A New Kind of Generalization
Year	2000
Data Source	CC BY-SA - https://paperswithcode.com